Superconductivity in Weyl Semimetal Candidate

Superconductivity in Weyl Semimetal Candidate MoTe2 Yanpeng Qi1, Pavel G. Naumov1, Mazhar N. Ali2, Catherine R. Rajamathi1, Oleg Barkalov1, Yan Sun1, Chandra Shekhar1, Shu-Chun Wu1, Vicky Süß1, Marcus Schmidt1, Eckhard Pippel2, Peter Werner2, Reinald Hillebrand2, Tobias Förster3, Erik Kampertt3, Walter Schnelle1, Stuart Parkin2, R. J. Cava4, Claudia Felser1, Binghai Yan1,5*, Sergiy A. Medvedev1* 1

Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany. IBM Almaden Research Center, San Jose, California 95120, USA. 3 Dresden High Magnetic Field Laboratory (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany. 4 Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA. 5 Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany. 2

Abstract In recent years, layered transition-metal dichalcogenides (TMDs) have attracted considerable attention because of their rich physics [1]; for example, these materials exhibit superconductivity [2,3], charge density waves [4], and the valley Hall effect [5,6]. As a result, TMDs have promising potential applications in electronics, catalysis, and spintronics [7−9]. Despite the fact that the majority of related research focuses on semiconducting TMDs (e.g., MoS2 [10]), the characteristics of WTe2 are provoking strong interest in semimetallic TMDs with extremely large magnetoresistance [11], pressure-driven superconductivity [12,13], and the predicted Weyl semimetal (WSM) state [14]. In this work, we investigate the sister compound of WTe2, MoTe2, which is also predicted to be a WSM [15] and a quantum spin Hall insulator in bulk and monolayer [16] form, respectively. We find that MoTe2 exhibits superconductivity with a resistive transition

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temperature Tc of 0.1 K. The application of a small pressure (such as 0.4 GPa) is shown to dramatically enhance the Tc, with a maximum value of 8.2 K being obtained at 11.7 GPa (a more than 80-fold increase in Tc). This yields a dome-shaped superconducting phase diagram. Further explorations into the nature of the superconductivity in this system may provide insights into the interplay between strong correlations and topological physics.

*

E-mail: [email protected]; [email protected]

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Transition-metal dichalcogenides (TMDs) typically share the same formula, MX2, where M is a transition metal (e.g., Mo or W) and X is a chalcogenide atom (S, Se, and Te). These compounds can crystallize in many structures, including 2H-, 1T-, 1T’-, and Td-type lattices. The most common structure is the 2H phase, where the transition-metal atoms are trigonal-prismatically coordinated by the chalcogenide atoms. These planes then stack upon one other with interspaced van der Waals (vdW) gaps. In contrast, the 1T structure corresponds to octahedral coordination of the transition metal. The 1T’ phase is a monoclinic lattice that can be interpreted as a distortion of the 1T phase by the formation of in-plane transition metal-metal bonds, resulting in a pseudo-hexagonal layer with zigzag metal chains. Finally, the Td phase is very similar to the 1T’ phase, but the layers stack in a direct fashion, resulting in a higher-symmetry orthorhombic structure. Depending on the synthesis technique, the same composition of MX2 can crystallize in a variety of structures with very different electronic properties. For example, MoTe2 can exist in 2H, 1T’, and Td structures [17−19], while WTe2 has commonly been observed in the Td structure [20]. The 2H and 1T compounds are primarily semiconducting, whereas the 1T’ and Td compounds are typically semimetallic. Very recently, semimetallic TMDs have attracted considerable attention because of the discovery of salient quantum phenomena. For instance, Td-WTe2 has been found to exhibit an extremely large magnetoresistance (MR) [11,21], pressure P-driven superconductivity (highest resistive transition temperature Tc ≈ 7 K at 16.8 GPa) [12,13], and a large and linear Nernst effect [22]. Further, this material has been theorized to constitute the first example of a “type-II” Weyl semimetal [14]. Additionally, the 1T’-MX2 monolayer has been predicted to be a 2D topological insulator (TI) [16].

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The discovery of superconductivity in WTe2 is apparently contradictory to previous theoretical predictions [23], which claim that 2H TMD may become superconducting under P, but the 1T’ phase will not. This has motivated the present authors to investigate another TMD, namely, MoTe2, for the appearance of superconductivity under applied P. This substance was chosen because it can exist in both the 2H and 1T’ phases, allowing for direct examination of this theory. To the best of our knowledge, no report has been published on P-induced superconductivity in MoTe2 to date. Further, if superconductivity exists in 1T’-MoTe2, it may allow the topological edge states to also become superconducting, because of their proximity to the bulk superconductor. This would supply a new platform for the study of topological superconductivity, which has potential application in quantum computation [24]. Regarding the recently anticipated Weyl semimetal (WSM) phase in MoTe2 [15], discovery of superconductivity may introduce a new pathway for the exploration of topological superconductivity [25−27] along with emergent space-time supersymmetry [28]. In this work, we report on the transport properties of the 2H, 1T’, and Td poly-types of MoTe2 under various applied P. We find that Td-MoTe2 exhibits superconductivity with Tc = 0.1 K, according to electrical resistivity ρ measurements. A small P (such as 0.4 GPa) dramatically enhances the Tc, and a dome-shaped superconducting phase diagram is observed with maximum Tc = 8.2 K at 11.7 GPa; this is approximately 80 times larger than the value at ambient P. In contrast, we do not observe any signature traces of superconductivity in the 2H phase under P, even when it becomes metallic. We assume that the extreme sensitivity of the superconductivity to P is a consequence of the unique electronic structure. Thus, MoTe2 presents the

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opportunity to study the interaction of topological physics and superconductivity in a bulk material. We first characterized 1T’-MoTe2 samples at ambient P using single-crystal X-ray diffraction (SXRD) and transmission electron microscopy (TEM). The atomic arrangement of the 1T’ structure was determined using high-resolution TEM images and diffraction patterns, as shown in Fig. 1a and b. The crystal structures of 1T’ and Td-MoTe2 are shown in Fig. 1c. At room temperature, the crystals exhibit the expected monoclinic 1T’-MoTe2 structure, while the measurements at 120 K indicate a transition into the orthorhombic Td structure. The TEM images confirm that the 1T’ structure crystallizes in the P21/m space group with lattice parameters of a = 0.6320 nm, b = 0.3469 nm, c = 1.386 nm, and β = 93.917º; these results are consistent with the previously reported structure [17]. The Raman spectra at ambient P contain two characteristic peaks (Fig. 4a), which are due to the Ag and Bg vibrational modes of the 1T’-MoTe2 structure; this is also in agreement with a previous report [29]. A full structural solution was obtained for the orthorhombic phase at 120 K, and the refinement values are given in Table SI. The ρ of MoTe2 down to a minimum temperature of Tmin = 0.08 K is shown in Fig. 2a. In contrast to the 2H phase, which displays semiconducting behavior, 1T’-MoTe2 is semimetallic in nature. At zero field, the room-temperature resistivity is ρ = 1.0 × 10−5 Ω m, which decreases to 2.8 × 10−7 Ω m at 0.5 K, yielding a residual resistance ratio (RRR) ~ 36. At temperature T = 250 K, an anomaly with thermal hysteresis (Fig. 2a, inset) is observed, which is associated with the first-order structural phase transition from 1T’ to Td-MoTe2 [19,30]. In addition, Td-MoTe2 gradually becomes superconducting below T = 0.3 K (the onset of transition), while zero resistance is

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observed at Tc = 0.1 K (Fig. 2b). Note that, although potential superconductivity at ~ 0.3 K in the titled compound has been briefly mentioned in the literature [31], no related data has been published prior to this paper. It is well known that applied P can effectively modify lattice structures and the corresponding electronic states in a systematic fashion. Hence, we measured ρ as a function of T for the same 1T’-MoTe2 single crystal at various P values. Fig. 3a shows the typical T dependence of ρ for P values of up to 34.9 GPa. For increasing P, the metallic characteristic increases and ρ decreases over the entire temperature range. Further, the ρ curve at low P exhibits an anomaly at a temperature of resistivity Ts of 185 K, which is associated with the structural phase transition (from monoclinic to orthorhombic upon cooling). With increasing P, the anomalous behavior in ρ is clearly suppressed and shifted to lower T. At P values above 4 GPa, the anomaly disappears completely. Thus, the application of P tends to stabilize the monoclinic phase. In addition, the Raman spectra recorded at room temperature under different P values (Fig. 4a) contain only two characteristic peaks for the 1T´-structure Ag and Bg modes [29]. The frequencies of both vibrational modes increase gradually with no discontinuities as P increases (Fig. 4b and c). This indicates normal mode behavior under compression. The stability of MoTe2 in different phases can be explained using total energy calculations within density-functional theory (DFT). After evaluating the total energies of the two phases, we found that the Td phase exhibits slightly lower energy (7 meV per formula unit) than the 1T’ phase. This is consistent with the fact that the low- and high-T phases are Td and 1T’, respectively, without external pressure. As the 1T’ phase can be obtained by sliding between vdW layers of the Td phase, the former exhibits a slightly smaller equilibrium volume than the latter, as revealed from the lattice

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parameters measured via SXRD. As illustrated by the energy-volume profile in Fig. 1d, the external P may stabilize the 1T’ phase with smaller volume (and correspondingly higher density) by enhancing the interlayer sliding. Pressure studies have also revealed that the Tc is very sensitive to the P value. That is, Tc increases dramatically to 5 K at relatively low P = 0.4 GPa, before beginning a slower increase to a maximum Tc of 8.2 K at 11.7 GPa (Fig. 3b). Beyond this P, the Tc begins to decrease and no superconductivity is observed down to 1.5 K at P values above 34.9 GPa (Fig. 3c). It should be noted that Ts is sharply reduced from 250 to 185 K at quite low P (0.4 GPa), while Tc simultaneously increases dramatically. Subsequently, both characteristic temperatures (Ts / Tc) vary (decrease / increase) slightly with increasing P. Our findings demonstrate that the strong enhancement of Tc under high P is associated with suppression of the structural phase transition. Further, we conducted ρ measurements in the vicinity of Tc for various external magnetic fields. As can be seen in Fig. 3d, the zero-resistance-point Tc under P = 11.2 GPa is gradually suppressed with increasing field, giving strong evidence that the transition

is

superconducting

in

nature.

Deviating

from

the

Werthamer-Helfand-Hohenberg theory based on the single-band model, the upper critical field of MoTe2 Hc2(T) has a positive curvature close to Tc (H = 0), as shown in Fig. 3e. This is similar to the behaviors of both WTe2 [12] and NbSe2 [32]. The experimental Hc2(T) data can be well approximated within the entire T range by the expression Hc2(T) = Hc2* (1 - T/Tc)1 + α [12,33]. The fitting parameter Hc2* = 4.0 T can be considered as the upper limit for the upper critical field Hc2(0), which yields a Ginzburg–Landau coherence length ξGL(0) of ~9 nm. The corresponding data obtained

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at P = 1.1 GPa is also shown in Fig. 3e. It is also worth noting that our estimated value of Hc2(0) is far beyond the Pauli-Clogston limit. We repeated the high-pressure experiments using different crystal flakes. Similar superconducting behavior with almost identical transition T values was observed, indicating that superconductivity is robust in MoTe2 under applied P. All the characteristic T values in the above experimental results are summarized in the T-P phase diagram shown in Fig. 5. Note that the Ts anomaly decreases rapidly with pressure. Further, the Tc(P) trend line increases rapidly to ~5 K at quite low P, and then continues to increase up to a maximum Tc,max = 8.2 K at a slow pace. This result is approximately 80 times larger than the value at ambient P. From this maximum, Tc begins to decrease with increasing P, with the transition eventually disappearing at P values of approximately 35 GPa. Thus, a dome-shaped superconducting phase boundary is obtained for MoTe2, with a sharp slope towards the low-P end of the diagram. For comparison with 1T’-MoTe2, we also measured ρ as a function of T for the 2H-MoTe2 single crystal and varying P. We found P-induced metallization at 15 GPa (see Fig. S2), which is consistent with previous theoretical predictions [23]. However, in contrast, we did not observe any signature traces of superconductivity in the 2H phase for P values of up to 40 GPa. For MoTe2, the superconducting behavior in the low-P region (≤ 0.4 GPa) clearly differs from that in the high-P region (> 0.4 GPa). Under quite low P, the sharp increase in Tc is concomitant with strong suppression of structural transitions, which is reminiscent of observations for Fe-based superconductors with various kinds of competing phase transitions [e.g., see Ref. 34]. For further increases of P, both Tc and Ts vary slightly. We found that the 1T’ phase exhibits a lower density of states (DOS) at

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the Fermi energy than that of the Td phase in the DFT calculations (see Fig. S6). Thus, one can expect that dramatic structural and electronic instabilities emerge in the low-P region, which may account for the strong enhancement of Tc. Thorough exploration of superconductivity in MoTe2 from both experimental and theoretical perspectives is required.

Methods 1T’-MoTe2 crystals were grown via chemical vapor transport using polycrystalline MoTe2 powder and TeCl4 as a transport additive [35]. Molar quantities of Mo (Sigma Aldrich 99.99%) were ground in combination with purified Te pieces (Alfa Aesar 99.99%), pressed into pellets, and heated in an evacuated quartz tube at 800 °C for 7 days. Crystals were obtained by sealing 1 g of this powder and TeCl4 (3 mg/ml) in a quartz ampoule, which was then flushed with Ar, evacuated, sealed, and heated in a two-zone furnace. Crystallization was conducted from (T2) 1000 to (T1) 900 °C. The quartz ampoule was then quenched in ice water to yield the high-temperature monoclinic phase. The obtained crystals were silver-gray and rectangular in shape. 2H-MoTe2 crystals were grown using a similar method, but without quenching. The structures of the MoTe2 crystals were investigated using single-crystal X-ray diffraction (SXRD) with Mo Ka radiation. In order to analyze the atomic structure of the material, transmission electron microscopy (TEM) was performed. The dependence of the electrical resistivity ρ on temperature T at ambient pressure P was measured using a conventional four-probe method (ac transport (ACT), physical property measurement system (PPMS), Quantum Design). Values of T down to 0.08 K were achieved using a home-built adiabatic demagnetization stage. The pulsed magnetic field experiments

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were conducted at the Dresden High Magnetic Field Laboratory (Hochfeld-Magnetlabor Dresden Helmholtz-Zentrum Dresden-Rossendorf (HLD-HZDR)). A non-magnetic diamond anvil cell (DAC) was used for ρ measurements under P values of up to 40 GPa. A cubic BN/epoxy mixture was used for the insulating gaskets and Pt foil was employed in the electrical leads. The diameters of the flat working surface of the diamond anvil and the gasket were 0.5 and 0.2 mm, respectively. The sample chamber thickness was ≈ 0.04 mm. The value of ρ was measured using the dc current van der Pauw technique in a customary cryogenic setup at zero magnetic field, and the magnetic field measurements were performed on a PPMS (ACT, Quantum Design). The P values were measured using the ruby scale, for small chips of ruby placed in contact with the sample [36]. The high-P Raman spectra were recorded using a customary micro-Raman spectrometer with an HeNe laser as the excitation source and a single-grating spectrograph with 1-cm-1 resolution. Density-functional theory (DFT) calculations were performed using the Vienna Ab-initio Simulation Package (VASP) with projected augmented wave (PAW) potential [37,38]. The exchange and correlation energy was considered at the generalized gradient approximation (GGA) level for the geometry optimization [39], and the electronic structure was calculated using the hybrid functional (HSE06) [40] with the inclusion of spin-orbital coupling. The band structures and Fermi surfaces were interpolated using the maximally localized Wannier functions (MLWFs) [41−43]. Acknowledgment Y. Qi acknowledges financial support from the Alexander von Humboldt Foundation. This work was financially supported by the Deutsche Forschungsgemeinschaft (DFG) (Project No. EB 518/1-1 of DFG-SPP 1666 "Topological Insulators") and by a

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European Research Council (ERC) Advanced Grant, No. (291472) "Idea Heusler".

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MoTe2. Phys. Rev. B 90, 035108 (2014). [24] Fu, L. et al. Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator. Phys. Rev. Lett. 100, 096407 (2008). [25] Cho, G. Y. et al. Superconductivity of doped Weyl semimetals: Finite-momentum pairing and electronic analog of the 3He-A phase. Phys. Rev. B 86, 214514 (2012). [26] Wei, H. et al. Odd-parity superconductivity in Weyl semimetals. Phys. Rev. B 89, 014506 (2014). [27] Hosur, P. et al. Time-reversal-invariant topological superconductivity in doped Weyl semimetals. Phys. Rev. B 90, 045130 (2014). [28] Jian, S.-K. et al. Emergent Spacetime Supersymmetry in 3D Weyl Semimetals and 2D Dirac Semimetals. Phys. Rev. Lett. 114, 237001 (2015). [29] Keum, D. H. et al. Bandgap opening in few-layered monoclinic MoTe2. Nature Phys. 11, 482–486 (2015). [30] Hughes, H. P. & Friend, R. H. Electrical resistivity anomaly in β–MoTe2. J. Phys. C: Solid State Phys. 11, L103-105 (1978). [31] Hulliger, F. Structure and bonding, Vol. 4, Springer-Verlag, Berlin, Heidelberg, New York 1968, p. 83. [32] Suderow, H. et al. Pressure induced effects on the Fermi surface of superconducting 2H-NbSe2. Phys. Rev. Lett. 95, 117006 (2005). [33] Müller, K. H. et al. The upper critical field in superconducting MgB2. J. Alloys Compd. 322, L10–13 (2001). [34] Stewart, G. R. Superconductivity in iron compounds. Rev. Mod. Phys. 83, 1589-1652 (2011). [35] Fourcaudot, G. et al. Vapor phase transport and crystal growth of molybdenum

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trioxide and molybdenum ditelluride. J. Cryst. Growth 46, 132-135 (1979). [36] Mao, H. K. et al. Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions. J. Geophys. Res. 91, 4673-4676 (1986). [37] Kresse, G. et al. Ab initio molecular dynamics for open-shell transition metals. Phys. Rev. B 48, 13115-13118 (1993). [38] Kresse, G. et al. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 6, 15-50 (1996). [39] Perdew, J. P. et al. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865 (1996). [40] Heyd, J. et al. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207-8215 (2003). [41] Marzari, N. et al. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847-12865(1997). [42] Souza, I. et al. Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001). [43] Mostofi, A. A. et al. Wannier 90: A tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685-699 (2008).

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Figure 1. MoTe2 crystal structure. a, TEM images of 1T’-MoTe2 along the [100] zone. The red rectangle shows the high-angle annular dark-field (HAADF) simulated image, and the red and blue spheres represent Te and Mo atoms, respectively. b, Corresponding electron diffraction images. c, 1T’ and Td-MoTe2 crystal structures. d, Energy-volume relation for 1T’ and Td-MoTe2.

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MoTe2 Cooling Warming

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Resistivity [10-6Ω m]


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220 240 260 280 Temperature [K]

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0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Temperature [K]

Figure 2. 1T’-MoTe2 resistivity at ambient pressure. a, Temperature-dependent resistivity at ambient pressure. Inset: Anomaly with hysteresis observed at approximately 250 K. This hysteresis is associated with the structural phase transition from 1T’-MoTe2 to Td-MoTe2. b, Resistivity detail from 0.08−1.2 K. Superconductivity

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is clearly observed for the Tc = 0.3 K.

Figure 3. Superconductivity evolution as a function of pressure. a, Electrical resistivity as a function of temperature for pressures of 0.76−34.9 GPa. The anomaly

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associated with the structural transition is completely suppressed with increasing pressure. b and c, Electrical resistivity as a function of temperature for pressures of 0.7−11.7 and 11.7−34.9 GPa, respectively. Clear electrical resistivity drops and zero-resistance behavior are apparent. Tc increases under increasing pressure and a dome-shaped superconducting phase in pressure-temperature space is observed for the maximum superconducting transition temperature corresponding to Tc = 8.2 K at 11.7 GPa. d, Temperature dependence of resistivity under different magnetic fields of up to 3 T at 11.2 GPa. e, Temperature dependence of MoTe2 upper critical field Hc2 determined using 90% points on resistivity transition curves. The red curve is the best-fit line.

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Figure 4. Raman spectra of 1T’-MoTe2. a, Pressure-dependent Raman signals for 1T’-MoTe2 at room temperature. The Raman spectra contain two characteristic peaks due to the Ag and Bg vibrational modes of the 1T’-MoTe2 structure. b and c, Peak positions (Ag and Bg, respectively) for various pressure values. The frequencies of both vibrational modes increase gradually and continuously as the pressure increases.

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Pressure [GPa] Figure 5. MoTe2 electronic phase diagram. The black square represents the structural phase transition temperature Ts. The red, blue, and olive circles represent the Tc extracted from various electrical resistance measurements.

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Temperature [K]

Temperature [K]

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